FISHERY BULLETIN: VOL. 87, NO. 4, 1989 



movements of its own prey base of smaller ani- 

 mals. We reasoned that it is unlikely that this 

 food chain is being swept along as rapidly as the 

 maximum current speeds, but, especially on 

 smaller scales, the distributions of prey and 

 predator are probably moving faster than the 

 speeds apparently characteristic of large-scale 

 seasonal movements. We chose 1 knot as a con- 

 servative appro.ximation. It is possible that 

 dolphin aggi'egating mechanisms move, over- 

 all, more slowly than 1 knot, but probably not 

 faster. Thus by comparing simulation results 

 from nonmoving topographies versus topog- 

 raphies moving at 1 knot, we have tried to 

 bracket the range of responses likely to occur in 

 the real system. 



In our model, dolphin schools were made to 

 respond to these topographies by adjusting 

 then- speed according to the quality level and by 

 adjusting their direction according to the 

 gradient in quality experienced during the pre- 

 vious time step. The range of speeds chosen for 

 dolphin schools (0.5 to 2.4 knots) was based on 

 average observed cruising speeds of dolphin 

 schools in the ETP'*. In the model, dolphin 

 speed is fastest at the lowest quality levels and 

 slowest at the highest quality levels. Direction 

 choice is stochastic with probabilities biased in 

 the forward direction when the gradient is 

 positive (conditions improving) and in the 

 reverse direction when the gi'adient is negative 

 (conditions deteriorating). Thus the rules for 

 school speed and direction cause schools to 

 circle slowly in "favorable" areas (i.e., on the 

 peaks) and to move rapidly straight ahead in 

 "unfavorable" areas (i.e., the valleys between 

 peaks). 



Vessel movements were controlled by each 

 vessel's history of dolphin school sightings, 

 through a "sightings memory" variable. The 

 value of the variable increases by one unit each 

 time a school is sighted and it decays constantly 

 by a given proportion with each time step. 

 Thus, the value of the variable will be high 

 when a vessel is in a "good" area (i.e., has seen 

 lots of schools) and will be low when the vessel 

 is in a "bad" area (schools are few). Vessel 

 direction is stochastic and affected by the value 

 of this "sightings memory" variable. When the 



value is high, direction choice is biased in the 

 reverse direction; i.e., the vessel is most Ukely 

 to turn appro -^'imately 180 degrees. When the 

 value is low, small angles are much more likely 

 to be chosen; i.e., the vessel will tend to con- 

 tinue moving forward. Each vessel maintains its 

 own sightings variable independent of the 

 sightings variables of other vessels, so that each 

 vessel moves independently of all other vessels. 



Generation of Simulated TVOD 



Each simulation began with totally random 

 distributions of both vessels and dolphin schools. 

 Nonrandom spatial distributions of vessels and 

 schools then developed as a function of the envi- 

 ronmental topography and of the movement 

 rules for schools and vessels. Each simulation 

 continued for 600 time steps of 1 h/step. 



Estimates of school abundance were based 

 only on TVOD collected during the last 200 

 steps. By this time, the model had in all cases 

 settled into a quasi-steady state (Fig. 3). TVOD 

 for each vessel, collected during each of these 

 last 200 steps, included vessel number, total 

 number of miles searched during that step, posi- 

 tion of the vessel at the end of the step, and 

 presence or absence of a school sighting. Only 

 one school could be sighted per vessel per time 

 step. 



TVOD were "collected" for all dolphin schools 

 moving within 2 nmi of any vessel. Two nautical 

 miles is the effective strip width found com- 

 monly with line transect analyses of real 

 TVOD.^'* All vessels were assumed to carry 

 observers. Observers were always on duty col- 

 lecting data (i.e., were never "off effort"). 

 Vessels searched continuously (i.e., did not stop 

 at "night"). 



Data Analyses 



TVOD were aggi'egated subsequently into 1° 

 squares prior to abundance estimation. One- 

 degree squares are the smallest geogi'aphic sub- 

 division that retains, with real TVOD, sufficient 

 data for hne transect analysis (Polachek 1983; 

 Buckland and Anganuzzi 1988). 



Four replicated simulations were conducted 

 for each of eight different cases representing two 



^Hedgepeth, J. 1985. Databa.se for dolphin tagging 

 operations in tlie eastern tropical Pacific, 1969-1978, with 

 discussion of 1978 tagging re.sults. Admin. Rep. No. LJ- 

 85-03. Southwest Fish. Cent., Natl. Mar. Fish. Serv., 

 NOAA, La Jolla, CA. 



'"M. Hall, Inter- American Tropical Tuna Commission, c/o 

 Scripps Institution of Oceanography, La Jolla, CA 92093, 

 pers. commuii. 



864 



